Where are the 4 aetherium shards located?

Additional Details:
Sometime after 1E 22, the Dwemer of Skyrim discovered a considerable source of raw Aetherium in Blackreach. [1]An alliance between four Dwemer cities of Arkngthamz, Raldbthar, Mzulft, and Bthar-zel (now known as Deep Folk Crossing) was created to oversee its extraction, processing, and study of the rare crystal.

Top Voted Answer

@ Deep Folk Crossing, go across the bridge and up the hill to a stone construction, where you find (or have already found) dwemer convector, helmet and sword. Go around the central stone, the shard is on the back.

Answers

You seem to have answered your own question. There is one piece at Deep Folk Crossing which is north of Markarth. One at Raldbthar which is west of Windhelm you have to go thru all the ruins to get it. One at Mzulft in the store room which is south east of Windhelm. One at Arkngthamz which is south east of Markarth again you have go all the way thru the ruins to get it.

You did answer your own question. Just go to each of those places. Katria doesn't mark the other 2 places after you get the first two shards because they're not really full dwemer ruins that you have to explore. The one shard is literally outside on a pedestal.

The first Aetherium Shard is located in the final room of Arkngthamz. The Dwemer Ruin is found south-east of Markarth, in the Reach.

The second Aetherium Shard is located in Deep Folk Crossing, more known also as Bthar-Zel. Deep Folk Crossing is north of Markarth in the Reach, and the shard is located across the bridge of Deep Folk Crossing.

The third Aetherium Shard is located in the Storage Room of Mzulft, which is found if you turn to the West before you enter the Dwemer ruin. I believe it has a high level lock guarding the entrance door. Mzulft is located to the far west of Skyrim, north-west of Riften.

The fourth Aetherium Shard is in Raldthbar, a massive and complex Dwemer ruin located slightly south-west of Windhelm. The Aetherium Shard is located in the final room of Raldthbar Deep Market, a sub-location of the great Dwemer ruin. All four should be relatively easy to locate once the Dwemer ruins have been discovered ( and entered ).